The classifying space of the one-dimensional bordism category and a cobordism model for TC of spaces
The classifying space of the one-dimensional bordism category and a cobordism model for TC of spaces
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一维边界范畴的分类空间和空间TC的共边界模型
DOI：
10.1112/topo.12179
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发表时间：
2020
影响因子：
1.1
通讯作者：
Steinebrunner J
中科院分区：
文献类型：
--
作者：
Steinebrunner J
边界型范畴的同伦范畴具有作为对象的闭合定向流形和作为模射的六维边界型的微分同胚类。利用一种新的本体类纤维序列，计算了for的分类空间，并将其表示为一个圆束。作为证明的一部分，我们构造了消去圆的协范畴的商。我们证明了这个范畴具有可分类的空间，而且，如果我们给这些界域配上到单连通空间的映射，所得到的结果可以被认为是拓扑循环同调的协配模型。在本文的第二部分，我们构造了一个无限循环空间映射，并利用它推导了表示Miller-Morita-Mumford类的有理环的组合公式。
The homotopy category of the bordism categoryhas as objects closed oriented‐manifolds and as morphisms diffeomorphism classes of‐dimensional bordisms. Using a new fiber sequence for bordism categories, we compute the classifying space offor, exhibiting it as a circle bundle over.As part of our proof, we construct a quotientof the cobordism category where circles are deleted. We show that this category has classifying spaceand moreover that, if one equips these bordisms with a map to a simply connected space, the resultingcan be thought of as a cobordism model for the topological cyclic homology.In the second part of the paper, we construct an infinite loop space mapin this model and use it to derive combinatorial formulas for rational cocycles onrepresenting the Miller–Morita–Mumford classes.